The given problem relates to the multivariable testing. The MVT
improves the quality of carbon-foam rings used in nuclear missile
housings. One type of defect analyzed was the number y of
black streaks in the manufactured ring. Two variables found to
impact the number of defects were turntable speed (revolutions per
minute),,
and cutting blade position (inches from center),.

a) It is given that the researcher discovered “an interaction
between blade position and turntable speed.” So, the appropriate
model to incorporate this interaction effect is,

Where y: Number of black streaks

Turntable speed

Blade position

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b) The researcher reported a positive linear relation between
the number of defects (y) and turntable speed ()
but found that the slope of the relationship was much steeper for
lower values of cutting blade position (),
this means that there is an importance for the interaction effect
in the fitted regression model for the data. Hence, we concentrate
more on interaction term in the model.